Yes, an ordinary meter will measure voltage up to its maximum frequency. Typically for DVMs that will be a few KHz.
You can rectify the signal and measure the resulting DC, this is how "field strength" meters work and the frequency limit is then decided by the physical properties of the signal path and the rectifier. F.S meters work up to hundreds of MHz.
The problem with simply amplifying and measuring is, as Andre pointed out, it 'sees' a mixture of all the signals within its bandwidth at once. The signals will be of many different frequencies and more importantly, many different phases. The signals don't add up in amplitude, as many as add up will subtract or partially subtract and you could even get an average of zero overall. It will work if only one signal is present (unlikely!) or if one signal is significantly stronger than all the others.
If you want to detect a radio signal and measure the voltage it produces, you need some kind of selective filter that only allows the one signal to get through and excludes all others. This is basically how a radio receiver works, you select the station you want with a tunable filter, amplify the selected frequency then 'detect' the amplitude or frequency shift to recover the audio.
Brian.